The Real Number SystemReal Numbers

Rational Numbers... -1.5, -1, -0.5, 0, 0.5, 1, 1.5, …

Integers... -3, -2, -1, 0, 1, 2, 3, …

Whole Numbers 0, 1, 2, 3, 4, 5, 6, …

Natural Numbers 1, 2, 3, 4, 5, 6, …

... 2, 1.816, 0, 1, 2, ... Irrational Numbers

2, 3, , 11...

The Real Number Line| | | | | | | | | | |

-5 -4 -3 -2 -1 0 1 2 3 4 5

Integers

-5 -4 -3 -2 -1 0 1 2 3 4 5

NaturalNumbers

-5 -4 -3 -2 -1 0 1 2 3 4 5

WholeNumbers

| | | | | | | | | | |-5 -4 -3 -2 -1 0 1 2 3 4 5 -4.5 -2.5 0.33 1.7 2.9 4.1

RationalNumbers

2 5

Irrational Numbers

Remember that Irrational Numbers

do not have an exact point on the number

line.

Square RootsA number is a Perfect Square if it is the product of two Identical Factors. 6 6 36

10 10 100 2 2 4

5 5 25 7 7 49

These are all perfect squares because they are the product of two identical factors.

Common Perfect SquaresHere is a list of the first 20 perfect

squares.

1

4

9

16

25

36

49

64

81

100

121

144

169

196

225

256

289

324

361

400

1

4

9

16

25

36

49

64

81

100

121

144

169

196

225

256

289

324

361

400

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I should probably try to remember those.

Evaluating Square Roots

Evaluate the following radicals

16 25 9 81

400 225 169 529

4 5 3 9

A number is a Perfect Square if it is the product of two Identical Factors.

20 15 13 23

More Evaluating Radicals

121 5.291681

2.8912.25

11 2.3 49

1.73.5

These are all Rational Numbers

15 20 90 803.87 4.47 9.49 8.94

These are all Irrational Numbers

More Irrational RootsIrrational Roots will always fall

between two consecutive integers.Between what two

consecutive integers is each square root?

35 130 217

Between5 and 6

Between-12 and -11

Between14 and 15

Asi De Facil That was easy

between144 2& 1 1

between25 & 36

between196 & 225

Homework

Page 20: 10 – 22 & 28 - 36Even Numbers Only

Expressing a Decimal as a Rational Number

Write the fraction as the given number over the place value. Reduce the resulting fraction if possible.0.3 0.225 0.2375 0.0325

310

2251,000

940

2,37510,000

1980

32510,000

13400

A rational number is any number that can be written in the form

ab

Expressing Rational Numbers as a DecimalA rational number is any

number that can be written in the form Common Fractions Decimal Fractions

Written with a numerator and a

denominator.1234116

To express as a decimal, perform the

division.

.5

.75

.0625

The numerator is written after the decimal point and the denominator is

indicated by the place value of the last digit.

0.5

0.75

0.0625

1510 2

7510

30 4

62510,0 100

16

These are all terminating decimals.

ab

Repeating Decimals

The same number, or pattern of numbers, repeats.13 0.3333333333 0.3

23 0.6666666667 0.6

49 0.4444444444 0.4

211

0.1818181818 0.18

433 0.1212121212 0.12

833 0.2424242424 0.24

That was easy

Symbols of InequalitySymbol

Example

Written in Words

9 2 9 is greater than 2

2 9 2 is less than 9

9 2 9 is greater than or equal to 2

2 9 2 is less than or equal to 9

2 9 2 is not equal to 9

Comparing Real NumbersCompare the following numbers with an inequality symbol.17, 143

Write each as

a decimal

4.1231, 4.3

Compare the

decimals4.1231 4.3

Write the answer with the original

numbers

117 43

253, 29

5.6 5., 3852

5.6 5.3852

25 293

43, 2

1.3 1., 4142

1.3 1.4142

4 23

711, 0.63

,0.63 0.63

0.63 0.63

7 0.6311

Ordering Numbers from Least to Greatest

Order the numbers in each group from least to greatest.

3.2 3.002 3.023.002 3.02 3.2

2.021 2.21 2.0021 2.21 2.021 2.0021

5 3 25 5 512 4 3

5.416 5.75 5.6

1 72 5 2.42 4

0.5 2 2.2361 1.75 2.4

2 1.75 0.5 2.2361 2.4

5 2 35 5 512 3 47 12 5 2.44 2

5.416 5.6 5.75

Homework

Page 20: 38 - 50Even Numbers

Only